"Under the Public Order Act [the police] have the powers to arrest you if you are using foul language if you are being abusive, quite right too.

"They've obviously decided not to go ahead with it but it shows the gravity of this offence."

The Prime Minister was yesterday accused by Labour of presiding over a “cover-up” after The Daily Telegraph published a 442-word police log stating that Mr Mitchell abused officers. The Chief Whip admits he behaved badly but denies the accuracy of the police report saying he called officers "f---ing plebs".

Conservative MPs are now openly casting doubt on Mr Mitchell’s future as Chief Whip, saying he has already infuriated new colleagues with “grand and pompous” behaviour.

Sources said Mr Mitchell has insisted on a getting a Government-funded ministerial car, even though his predecessor, Patrick McLoughlin, did not have one.

He has also raised eye-brows by ordering a re-design of his Chief Whip’s office. Shortly after moving job, he asked for new furniture and shunned the traditional Chief Whip’s desk used by former Prime Ministers William Gladstone and Benjamin Disraeli

They said he has also requested new paintings for his room from the Government art department.

Colleagues said the minister’s temper has been even shorter than usual since his demotion from Development Secretary to Chief Whip, as he lost the perks of being a cabinet minister.

However, others said Mr Mitchell was also difficult to work with in the Department for International Development. One source said he kept a “joke machine” that said “bulls--t” to humiliate colleagues at the touch of a button during his time there.

A senior backbench MP last night said Mr Mitchell’s behaviour made him unsuitable to be a whip in charge of disciplining the party.

“The chief whip needs to be good at intelligence gathering and gentle persuading, not shouting at people,” he said. “People are already saying if he tries to impose discipline we’ll tell him to f—off in his own language.”

A spokesman for the Cabinet Office said “it’s true that Mr Mitchell has had discussions about the use of a ministerial car for himself and his fellow whips”.

“As with many ministers post-reshuffle, he’s inherited an office and made some changes,” the spokesman said.

In a new survey by YouGov, the majority of the public think Mr Mitchell should resign. Just over 50 per cent of 1,700 people questioned said he should stand down, while almost 70 per cent accepted the police account of the incident.

Despite publicly backing Mr Mitchell, Downing Street is anxious to make sure the Chief Whip’s outburst has not upset backbenchers.

It is understood a senior aide to Mr Cameron phoned a number of Conservative MPs to gather their views on the incident after it became public.

Even if Conservatives are willing to forgive Mr Mitchell, senior Liberal Democrats appeared reluctant to close the issue.

Vince Cable, the Business Secretary, joked in his speech at the party’s conference this week that he was a “mere pleb”.

Jeremy Browne, the Lib Dem Home Office minister, also said Mr Mitchell needed to tie up the “loose ends”.

“I know there’s a big media debate about what this says about the Conservative Party; whether it means the Conservatives are out of touch and whether they sound like they’re talking down to people,” he said.